A 1.5 spider is dangling at the end of a silk thread. You can make the spider bounce up and down on the thread by tapping lightly on his feet with a pencil. You soon discover that you can give the spider the largest amplitude on his little bungee cord if you tap exactly once every 3 seconds.

What is the approximate spring constant of the silk thread?

Use T= 2pi(sqrt(m/k))

Solve for k

.010966277

To calculate the spring constant of the silk thread, we can use the formula:

k = (4π²m)/T²

where:
k is the spring constant,
m is the mass of the spider (1.5 g, but we need to convert it to kg),
T is the time period between each tap (3 seconds).

1. Convert the mass of the spider from grams to kilograms:
mass in kg = 1.5 g / 1000 = 0.0015 kg

2. Plug the values into the formula:
k = (4π² * 0.0015 kg) / (3 seconds)²

3. Calculate the square of 3 seconds:
(3 seconds)² = 3² = 9 seconds²

4. Calculate the value of π (pi):
π ≈ 3.14159

5. Substitute the values into the formula:
k = (4 * 3.14159² * 0.0015 kg) / 9 seconds²

6. Simplify the equation:
k ≈ 0.00166 N/m

Therefore, the approximate spring constant of the silk thread is 0.00166 N/m.

To determine the approximate spring constant of the silk thread, we can use the relationship between the period (T) and the spring constant (k) for a simple harmonic oscillator.

The period is the time taken for one complete oscillation or cycle. In this case, the period is given as 3 seconds.

The formula for the period of a simple harmonic oscillator is given by:

T = 2π√(m/k)

Where:
T = Period
m = Mass of the object attached to the spring
k = Spring constant

In this scenario, the mass of the spider (m) is not provided. However, since we are concerned with the spring constant (k), we can assume that the mass of the spider is constant throughout.

Now, we need to rearrange the equation to solve for the spring constant (k):

k = (4π^2 * m) / T^2

Since we don't know the exact mass (m) of the spider, we'll use a general approximation of the spring constant.

Typically, the mass of a spider with a leg span of 1.5 cm would be around 0.1 grams (or 0.0001 kg). So, let's assume the mass (m) as 0.0001 kg.

Substituting the values in the equation:

k = (4π^2 * 0.0001) / (3^2)
k = 0.00277 N/m (approximately)

Therefore, the approximate spring constant of the silk thread is 0.00277 N/m.